Rebels in Congo have pulled out of a town on the Ugandan border they captured in fighting that forced 10,000 people to flee, the U.N. and a spokesman for the insurgents said Tuesday.

Rebels withdrew from Ishasha on Sunday because "we wanted to show that we are for peace and our objective is not to take other areas," spokesman Bertrand Bisimwa said.

A spokesman for the 17,000-strong U.N. peacekeeping mission, Lt. Col. Jean-Paul Dietrich, confirmed that rebels had withdrawn from the town.

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The offensive was meant to expel some of the perpetrators of Rwanda's 1994 genocide, but forced thousands of civilians to flee eastern Congo to neighboring Uganda. The rebels argue that Hutus who fled to Congo after the genocide were the targets of attacks — not the Congolese army.

But U.N. special envoy Olusegun Obasanjo berated rebel leader Laurent Nkunda for starting the offensive last month in violation of a cease-fire. Regional leaders fear such clashes could draw in Congo's neighbors as they did in Congo's 1998-2002 war, which engulfed armies from six African nations anxious for a share of Congo's vast mineral riches.

Nkunda, a former general, quit Congo's army in 2004 to launch a rebellion. Critics say Nkunda is more interested in power and the country's wealth than in protecting minority Tutsis.

Bisimwa said the unilateral cease-fire called by the rebels only applied to Nkunda's forces and the army, and not to the Hutu fighters or Congolese militias known as the Mai Mai, who have both been de facto allies of the army in the war with Nkunda.

Bisimwa said rebels had withdrawn from the area along Lake Edward and also pulled troops out of the village of Nyakokoma. He said no U.N. forces were deployed in the area and said they should be because Hutu militias who were pushed back could easily return.

Some refugees already have fled three or four times since years of low-level fighting in eastern Congo intensified with a rebel offensive in August. More than 250,000 people have abandoned their homes since then.